1. Mix all the sauce ingredients in a saucepan and let simmer over low heat for about 20 minutes, stirring occasionally to prevent sticking.
2. Meanwhile, sauté mushrooms in a little bit of oil until they have softened and become flavorful.
3. Cook pasta in boiling, salted water to al dente, or according to package directions. Drain well.
4. Remove sprig of rosemary, if using, from the sauce and pour the sauce over the hot pasta. Mix well. Add mushrooms and toss.
5. Top with a large handful of chopped parsley and a few more twists of a black pepper grinder. Best if mixed right before serving. You can keep sauce warm in a pot separately until ready to serve.